March 3, 2006
Contents
1 BREWSTER’S ANGLE
2
2 INVERSE SQUARE LAW FOR LIGHT
7
3 POLARIZATION OF LIGHT
11
4 INTERFERENCE AND DIFFRACTION OF LIGHT
16
5 MICROWAVE OPTICS
26
1
Chapter 1
BREWSTER’S ANGLE
Introduction
In this experiment, light is partially polarized when reflected off a nonconducting surface
and Brewster’s angle is measured.
Light from a diode laser is reflected off the flat side of an acrylic semi-circular lens. The
reflected light passes through a polarizer and is detected by a light sensor. The angle of
reflection is measured by a Rotary Motion Sensor mounted on the Spectrophotometer table.
The intensity of the reflected polarized light versus reflected angle is graphed to determine
the angle at which the light intensity is a minimum. This is Brewster’s Angle, which is used
to calculate the index of refraction of acrylic.
Equipment Needed
Brewster’s Angle Accessory
Educational Spectrophotometer System
Diode Laser
ScienceWorkshop 750 Interface
DataStudio Software
Theory
When unpolarized light reflects off a nonconducting surface, it is partially polarized parallel
to the plane of the reflective surface. There is a specific angle called Brewster’s angle at
which the light is 100% polarized. This occurs when the reflected ray and the refracted ray
are 90 degrees apart.
According to Snell’s Law,
n1 sin θ1 = n2 sin θ2
(1)
2
Figure 1.1:
where n is the index of refraction of the medium and θ is the angle of the ray from the
normal.
When the angle of incidence is equal to Brewster’s angle, θp ,
n1 sin θp = n2 sin θ2
(2)
and since θp + θ2 = 90o ,
θ2 = 90o − θp
and sin θ2 = sin(90o − θp ) = sin 90o cos θp − cos 90o sin θp = cos θp
Substituting for sin θ2 in Equation (2) gives
n1 sin θp = n2 cos θp
Therefore,
n2
= tan θp
n1
(3)
Setup
1. Attach the spectrophotometer table to the track. Put the diode laser, 2 polarizers and
the collimating slits on the track as shown in Figure. Mount the Rotary Motion Sensor with
3
the bigger dimeter of spindle against the spectrophotometer table (see figure). Attach the
spectrophotometer table base to ground as instructed by your teacher.
Figure 1.2:
2. The spectrophotometer disk should be put on ”backwards” with the 180 degree mark at
the position where the zero mark is normally.
3. Two round polarizers are used on the holder. Rotate the second polarizer (second from
laser) to 45 degrees and lock it in place by tightening the brass screw. The first polarizer
(closest to the laser) is used throughout the experiment to adjust the light level. Since
the ratio of reflected light to incident light is measured, better data will be obtained if the
incident light level is kept above 50%.
4. The square analyzing polarizer has its transmission axis marked, and for normal use the
label should be on top with its axis horizontal and thus 90 degrees from the polarization
axis of the reflected light. This is finding the variation in the ”p” (parallel) component of
the reflected light and is used to determine Brewster’s angle and to calculate the index of
refraction. But by placing the analyzing polarizer with its transmission axis vertical, you
can also look at the variation in the ”s” (perpendicular) component of the reflected light as
well.
5. The 45 degree polarizer is used to solve the problem that the laser light is already
polarized. To make the relative intensities of the s and p components the same, the light is
polarized at 45 degrees.
6. The small metal Brewster’s angle base disk should be screwed in and zeroed so that the
mark at the top of the label above the N in the word ANGLE is aligned with the zero angle
mark on the spectrophotometer disk.
7. The plastic base has two zero marks. For reflected light, use the mark that is on the side
with the higher step. The D lens is placed on the lower surface flush against the step when
4
data is being collected. The other mark would be used for transmission, like for Snell’s Law.
8. To align the laser beam, remove all polarizers, collimating slits, and D lens. Set the
spectrophotometer arm on 180 degrees. Use the x-y adjust on the laser to get the laser
beam at the center of the Light Sensor slit. The Light Sensor bracket slit should be set on
#4. Place the collimating slits on track and adjust the slit position so the laser beam passes
through the #4 slit.
9. Plug the Rotary Motion Sensor into Channels 1 and 2 on the ScienceWorkshop 750 Interface. Plug the Light Sensor into Channel A. Open the DataStudio file called ”Brewsters”.
Procedure
1. With the D lens removed, zero the angle for Rotary Motion Sensor: Rotate the spectrophotometer arm so the laser beam is centered on the Light Sensor slit. The spectrophotometer
disk should be near 180 degrees but it doesn’t matter if it is slightly off. Click on START and
move the arm back and forth in front of the laser, watching the intensity on the computer.
Stop at the position that gives the maximum intensity. Click on STOP and do not move the
arm until program is started to take the actual data run. This insures that zero for Rotary
Motion Sensor is at the center of the beam. Place D lens on the platform against the step.
Note about angle measurement: The angle is computed by dividing the actual angle
(recorded by the computer) by two. The best procedure is to move the spectrophotometer
arm, reading the angle on the digits display, and then rotate the plastic Brewster’s disk to
match same angle. Thus the markings on Brewster’s disk are only there for convenience (in
this experiment) and are not used directly. But, to get the laser beam exactly on to the slit,
you must make fine adjustments while watching the digits display for the maximum light
intensity. You can adjust either the disk or the spectrophotometer arm until the intensity is
maximized.
2. Turn out the room lights. A small light might be useful for seeing the computer keys to
type in values and to put the analyzing polarizer on and off. Click on START. Do not click
on STOP until all of the procedure steps are completed. Set angle to 85 degrees. The square
analyzing polarizer should not be in place. Rotate the Brewster disk to about 85 and, while
watching the digits display of light intensity, fine tune the position to get into the beam.
It doesn’t have to be exact, just so that you get enough light. Rotate the first polarizer
(nearest to the laser) to adjust the level to be as high as possible without exceeding 90%.
The Light Sensor should be on gain of 1 or 10.
3. Enter the angle into the table. Read the digits display of the light intensity and record
the value under ”Total Light” column. Place square analyzing polarizer (axis horizontal) on
the arm just in front of slits. (Note: The square analyzing polarizers must sit level, flat on
the arm.) Read the digits display of light intensity and record value under ”Polarized Light”
5
column. You must hit enter after typing each value. Check to see if the value is plotted on
the graph.
4. Remove the analyzing polarizer and go to the next angle, in increments of 5 degrees.
Since the results are live on the graph, you can see when the intensity is approaching the
minimum. Take data points every 1 degree near the minimum. At low intensities (below
2%), it is useful to switch the gain on sensor up by factor of 10. Note that you must divide
the measured intensity by 10 to get the correct value, but this method gives much better
results.
5. Click on ”Fit” at the top of the graph and choose the polynomial fit. Determine the angle
at which the reflection is a minimum. This is Brewster’s angle.
Analysis
1. Use Brewster’s angle to calculate the index of refraction of acrylic using Equation (3).
What value should you plug in for n1 ?
2. Would Brewster’s angle be more or less for light in air reflecting off water?
3. How do polarized sunglasses reduce glare? Which direction is the axis of polarization in
a pair of polarized sunglasses? How could you check this?
6
Chapter 2
INVERSE SQUARE LAW FOR
LIGHT
Introduction
The relative light intensity versus distance from a point light source is plotted. As the Light
Sensor is moved by hand, the string attached to the Light Sensor that passes over the Rotary
Motion Sensor pulley to a hanging mass causes the pulley to rotate, measuring the position.
Using DataStudio, various curves are fitted to the data to see which fits better.
Equipment
Basic Optics System (Track and 4-in-1 Light Source)
Aperture Bracket
20g hooked mass
Thread
Light Sensor
Rotary Motion Sensor
ScienceWorkshop 750 Interface
DataStudio Software
Theory
If light spreads out in all directions, as it does from a point light source, the intensity at a
certain distance from the source depends on the area over which the light is spread. For a
sphere of radius r, what is the equation for the surface area?
Intensity is calculated by taking the power output of the bulb divided by the area over which
the light is spread:
7
Intensity =
P ower
Area
Put the surface area of a sphere into the intensity equation. How does the intensity of a
point source depend on distance?
Setup
Figure 2.1:
1. Set up the equipment as shown in the figure. The thread is attached to the Light Sensor
bracket and passes over the large pulley to a hanging 10g mass.
2. Plug the Rotary Motion Sensor into Channels 1 and 2 on the ScienceWorkshop 750
interface and plug the Light Sensor into Channel A.
3. Start the DataStudio program and open the file called ”Light Intensity”.
Procedure
I. Exploring Different Functions
1. Click on the graph called Functions. This graph shows y = x.
2. Click on the calculator button at the top of the graph.
3. Change the function in the calculator window to y = x2 and click accept. Examine the
resulting changes in the graph. Note the shape of the graph.
4. Change the function in the calculator window to y = 1/x, click accept, and examine the
new graph.
5. Change the function in the calculator window to y = 1/x2 , click accept, and examine the
new graph. Now that you have familiarized yourself with these different functions you are
ready to plot the light intensity vs. distance for a point light source.
8
II. Adjusting the Sensitivity of the Light Sensor
The sensitivity of the Light Sensor must be adjusted so it does not max out or so it is not
set so low that the signal is poor.
1. Set the front of the Light Sensor mask 15cm from the center of the point light source.
Note that you must sight down the front of the Light Sensor mask to see where it lines up
with the track measuring tape. The center of the point light source is indicated by the notch
in the light source bracket. Plug in the point light source.
2. Rotate the aperture bracket to the white circle.
3. Press the Start button above and monitor the voltage output from the Light Sensor.
Adjust the gain switch on the top of the Light Sensor so the voltage is as close to 4.5V as
possible without exceeding 4.5V .
III. Taking the Intensity vs. Distance Data:
1. With the Light Sensor 15cm from the center of the light bulb, click on START. Squeeze
the sides of the Light Sensor slowly from 15cm to 100cm away from the bulb. As you do this,
the thread will rotate the Rotary Motion Sensor, recording the distance the Light Sensor is
from the bulb.
2. Try moving the Light Sensor away from the light bulb now and check to make sure the
distance is positive. If it is negative, exchange the Rotary Motion Sensor plugs in the 750
interface. Then click on STOP. Return the Light Sensor mask to the 15cm position.
3. With the Light Sensor mask at 15cm, click on START to take data. Slowly pull the Light
Sensor back from 15cm to about 100cm or until the hanging mass touches the floor.
4. Press the upper left button on the Light Intensity vs. Distance graph to scale the data
so it fits the whole graph.
5. Choose the various fits (linear, square fit, inverse fit, inverse square fit) from the pull-down
Fit menu on the graph. For each fit, record the error given in the fit box.
6. The best fit is the one which has the least error. Which fit best for the point source?
How does the light intensity depend on distance?
7. Do your results agree with your prediction from the theory?
8. Sketch the graph with the best fit or, if a printer is available, print it.
9
Question
Suppose you repeated this experiment with a long fluorescent bulb and the Light Sensor is
moved along the axis perpendicular to the light bulb. Would you expect the light intensity
for this line of light to depend on distance in the same way as it does for a point light source?
Why or why not? What dependence on distance would you expect?
10
Chapter 3
POLARIZATION OF LIGHT
Purpose
To determine the relationship between the intensity of the transmitted light through two
polarizers and the angle, φ, of the axes of the two polarizers.
Theory
A polarizer only allows light which is vibrating in a particular plane to pass through it. This
plane forms the ”axis” of polarization. Unpolarized light vibrates in all planes perpendicular
to the direction of propagation. If unpolarized light is incident upon an ”ideal” polarizer,
only half will be transmitted through the polarizer. Since in reality no polarizer is ”ideal”,
less than half the light will be transmitted.
The transmitted light is polarized in one plane. If this polarized light is incident upon a
second polarizer, the axis of which is oriented such that it is perpendicular to the plane of
polarization of the incident light, no light will be transmitted through the second polarizer.
However, if the second polarizer is oriented at an angle so that it is not perpendicular to
the first polarizer, there will be some component of the electric field of the polarized light
that lies in the same direction as the axis of the second polarizer, thus some light will be
transmitted through the second polarizer (See Figure 3-1).
The component, E, of the polarized electric field, Eo , is found by:
E = Eo cos φ
Since the intensity of the light varies as the square of the electric field, the light intensity
transmitted through the second filter is given by:
I = Io cos2 φ
11
where Io is the intensity of the light passing through the first filter and φ is the angle between
the polarization axes of the two filters.
Consider the two extreme cases illustrated by this equation:
• If φ is zero, the second polarizer is aligned with the first polarizer, and the value of cos2 φ
is one. Thus the intensity transmitted by the second filter is equal to the light intensity that
passes through the first filter. This case will allow maximum intensity to pass through.
• If φ is 90o , the second polarizer is oriented perpendicular to the plane of polarization of
the first filter, and the cos2 (90o ) gives zero. Thus no light is transmitted through the second
filter. This case will allow minimum intensity to pass through.
These results assume that the only absorption of light is due to polarizer effects. In fact
most polarizing films are not clear and thus there is also some absorption of light due to the
coloring of the Polaroid filters.
Figure 3.1:
12
Equipment Needed
Basic Optics Bench
Basic Optics Light Source
Light Sensor
Rotary Motion Sensor
Aperture Bracket
Procedure
A. Equipment Setup
Figure 3.2:
In this activity, the Light Sensor measures the relative intensity of light that passes through
two polarizers. You will change the angle of the second polarizer relative to the first. The
Rotary Motion Sensor measures the angle.
The ScienceW orkshop program records and displays the light intensity and the angle between the axes of the polarizers. You can use the program’s built-in calculator to compare
the relative intensity to the angle, the cosine of the angle, and the cosine2 of the angle.
1. Mount the Basic Optics Light Source, Polarizer holder, Polarizer Analyzer with Rotary
Motion Sensor, and Aperture Bracket holder with Light Sensor as shown.
2. Connect the ScienceW orkshop interface to the computer, turn on the interface. Start
ScienceW orkshop.
13
3. Connect the Light Sensor cable to Analog Channel A. Connect the Rotary Motion Sensor
cable to Digital Channels 1 and 2.
B. Experiment Setup
Select the Sensors and Set the Sample Rate
Refer to the User’s Guide for your version of ScienceW orkshop for detailed information on
selecting sensors and changing the sample rate.
1. In the Experiment Setup window, select the Rotary Motion Sensor and connect it to
Digital Channels 1 and 2.
2. Set up the Rotary Motion Sensor for high resolution. Select Large P ulley (Groove) for
the linear calibration.
3. In the Experiment Setup window, select the Light Sensor and connect it to Analog
Channel A.
4. Set the sample rate to 20Hz, or 20 measurements per second.
Select the Display
Refer to the User’s Guide for your version of ScienceW orkshop for detailed information on
selecting and changing displays.
1. Select a Graph display.
2. Set the axes of the Graph display so light intensity is on the vertical axis and angular position
is on the horizontal axis.
Prepare to Record Data
Refer to the User’s Guide for your version of ScienceW orkshop for detailed information on
monitoring and recording data.
1. Turn both Polarizers so they are at the same beginning angle (e.g., zero degrees).
2. Start monitoring data.
3. Rotate one Polarizer back and forth until the transmitted light intensity is maximum.
4. Stop monitoring data.
14
Record Data
1. Start recording data.
2. Slowly rotate the Polarizer on the Polarization Analyzer in the clockwise direction. Continue to rotate the Polarizer until you have made one complete rotation (360 degrees).
3. After one complete rotation, stop recording data.
Analyze the Data
Refer to the User’s Guide for your version of ScienceW orkshop for detailed information on
creating and displaying calculations and using ScienceW orkshop for data analysis.
1. Use the Experiment Calculator in the ScienceW orkshop program to create a calculation
of the cosine of the angle between the Polarizers.
2. Repeat the procedure to create a calculation of the cosine2 of the angle of the Polarizers.
3. Use the Graph display to examine the plot of light intensity versus angle.
4. Change the Graph display to show the plot of light intensity versus the cosine of the angle,
and then change the Graph display to show the plot of light intensity versus the cosine2 of
the angle.
5. Use the ScienceW orkshop program to determine the relationship between the light
intensity and the cosine2 of the angle.
Questions
1.What is the shape of the plot of light intensity versus angle?
2. What is the shape of the plot of light intensity versus cosine of the angle?
3. What is the shape of the plot of light intensity versus cosine2 of the angle?
4. Theoretically, what percentage of incident plane polarized light would be transmitted
through three Polarizers which have their axes rotated 17 degrees (0.29 radians) frpm each
other? Assume ideal polarizers and assume that the second polarizer’s axis is rotated 17
degrees (0.29 radians) from the first and that the third polarizer’s axis is rotated 17 degrees
(0.29 radians) from the second.
5. From your data, determine the answer to Question 4 for the real polarizers.
15
Chapter 4
INTERFERENCE AND
DIFFRACTION OF LIGHT
Experiment 1: Diffraction from a Single Slit
Purpose
To examine the diffraction pattern formed by laser light passing through a single slit and verify that the positions of the minima in the diffraction pattern match the positions predicted
by theory.
Equipment Needed
Track and Screen from the Basic Optics System
Diode Laser
Single Slit Disk
White paper to cover screen
Metric rule
Theory
When diffraction of light occurs as it passes through a slit, the angle to the minima in the
diffraction pattern is given by
a sin θ = mλ
(m = 1, 2, 3, ...)
where a is the slit width, θ is the angle from the center of the pattern to the mth minimum,
λ is the wavelength of the light, and m is the order (1 for the first minimum, 2 for the second
minimum, ... counting from the center out). See Figure 4.1.
Since the angles are usually small, it can be assumed that
sin θ ≈ tan θ
16
Figure 4.1: Single Slit Diffraction Pattern
From trigonometry,
tan θ =
y
D
where y is the distance on the screen from the center of the pattern to the mth minimum
and D is the distance from the slit to the screen as shown in Figure 4.1. The diffraction
equation can thus be solved for the slit width:
a=
mλD
y
(m = 1, 2, 3, ...)
Setup
1. Set up the laser at one end of the optics bench and place the Single Slit Disk in its holder
about 3cm in front of the laser. See Figure 4.2.
2. Cover the screen with a sheet of paper and attach it to the other end of the bench so that
the paper faces the laser.
3. Select the 0.04mm slit by rotating the slit disk until the 0.04mm slit is centered in the
slit holder. Adjust the position of the laser beam from left-to-right and up-and-down until
the beam is centerd on the slit.
Procedure
1. Determine the distance from the slit to the screen. Note that the slit is actually offset
from the center line of the slit holder. Rrecord the screen position, slit position, and the
difference between these (the slit-to-scren distance) in Table 4.1.
17
Figure 4.2: Optics Bench Ssetup
2. Turn off the room lights and mark the positions of the minima in the diffraction pattern
on the screen.
3. Turn on the room lights and measure the distance between the first order (m = 1) marks
and record this distance in Table 4.1. Also measure the distance between the second order
(m = 2) marks and record in Table 4.1.
Table 4.1 Data and Results for the 0.04mm Single Slit
Slit-to-screen distance (D)=.............................
First Order (m = 1) Second Order (m = 2)
Distance between side orders
Distance from center to side (y)
Calculated slit width
% difference
4. Make a sketch of the diffraction pattern to scale.
5. Change the slit width to 0.02mm and 0.08mm and make sketches to scale of each of these
diffraction patterns.
Analysis
1. Divide the distances between side orders by two to get the distances from the center of
the pattern to the first and second order minima. Record these values of y in Table 4.1.
2. Using the average wavelength of the laser (670nm for the Diode Laser), calculate the slit
width twice, once using first order and once using second order. Record the results in Table
4.1.
3. Calculate the percent differences between the experimental slit widths and 0.04mm.
Record in Table 4.1.
Question
Does the distance between minima increase or decrease when the slit width is increased?
18
Experiment 2: Interference from a Double Slit
Purpose
To examine the diffraction and interference patterns formed by laser light passing through
two slits and verify that the positions of the maxima in the interference pattern match the
positions predicted by theory.
Equipment Needed
Track and Screen from the Basic Optics System
Diode Laser
Multiple Slit Disk
White paper to cover screen
Metric rule
Theory
When light passes through two slits, the two light rays emerging from the slits interfere with
each other and produce interference fringes. The angle to the maxima (bright fringes) in the
interference pattern is given by
d sin θ = mλ
(m = 0, 1, 2, 3, ...)
where d is the slit separation, θ is the angle from the center of the pattern to the mth
maximum, λ is the wavelength of the light, and m is the order (0 for the central maximum,
1 for the first side maximum, 2 for the second side maximum, ... counting from the center
out). See Figure 4.3.
Since the angles are usually small, it can be assumed that
sin θ ≈ tan θ
From trigonometry,
tan θ =
y
D
where y is the distance on the screen from the center of the pattern to the mth maximum
and D is the distance from the slits to the screen as shown in Figure 4.3. The interference
equation can thus be solved for the slit separation:
d=
mλD
y
(m = 0, 1, 2, 3, ...)
19
Figure 4.3: Interference Fringes
While the interference fringes are created by the interference of the light coming from the
two slits, there is also a diffraction effect occuring at each slit due to Single Slit diffraction.
This causes the envelope as seen in Figure 4.4.
Figure 4.4: Single Slit Diffraction Envelope
Setup
1. Set up the laser at one end of the optics bench and place the Multiple Slit Disk in its
holder about 3cm in front of the laser. See Figure 4.5.
2. Cover the screen with a sheet of paper and attach it to the other end of the bench so that
the paper faces the laser.
20
Figure 4.5: Optics Bench Setup
3. Select the double slit with 0.04mm slit width and 0.25mm slit separation by rotating the
slit disk until the desired double slit is centered in the slit holder. Adjust the position of the
laser beam from left-to-right and up-and-down until the beam is centered on the double slit.
Procedure
1. Determine the distance from the slits to the screen.
Note that the slits are actually offset from the center line of the slit holder. Record the
screen position, slit position, and the difference between these (the slit-to-screen distance)
in Table 4.2.
2. Turn off the room lights and mark the positions of the maxima in the interference pattern
on the screen.
Table 4.2 Data and Results for the 0.04mm/0.25mm Double Slit
Slit-to-screen distance (D)=.............................
First Order (m = 1) Second Order (m = 2)
Distance between side orders
Distance from center to side (y)
Calculated slit width
% difference
3. Turn on the room lights and measure the distance between the first order (m = 1) marks
and record this distance in Table 4.2. Also measure the distance between the second order
(m = 2) marks and record in Table 4.2.
4. Make a sketch of the interference pattern to scale.
5. Change to a new double slit with the same slit width (0.04mm) but different slit separation
(0.50mm) and make a sketch to scale of this new interference pattern.
21
6. Change to another double slit with a slit width of 0.08mm and the original slit separation
(0.25mm) and make a sketch to scale of this new interference pattern.
Analysis
1. Divide the distances between side orders by two to get the distances from the center of
the pattern to the first and second order maxima. Record these values of y in Table 4.2.
2. Using the average wavelength of the laser (670nm for the Diode Laser), calculate the slit
separation twice, once using first order and once using second order. Record the results in
Table 4.2.
3. Calculate the percent differences between the experimental slit separation and 0.25mm.
Record in Table 4.2.
Questions
1. Does the distance between maxima increase, decrease or stay the same when the slit
separation is increased?
2. Does the distance between maxima increase, decrease or stay the same when the slit
width is increased?
3. Does the distance to the first minima in the diffraction envelope increase, decrease or stay
the same when the slit separation is increased?
4. Does the distance to the first minima in the diffraction envelope increase, decrease or stay
the same when the slit width is increased?
22
Experiment 3: Comparisons of Diffraction and Interference Patterns
Purpose
To compare the diffraction and interference patterns formed by laser light passing through
various combinations of slits.
Equipment Needed
Track and Screen from the Basic Optics System
Diode Laser
Single and Multiple Slit Disks
White paper to cover screen
Theory
When diffraction of light occurs as it passes through a slit, the angle to the minima in the
diffraction pattern is given by
a sin θ = mλ
(m = 1, 2, 3, ...)
where a is the slit width, θ is the angle from the center of the pattern to the mth minimum,
λ is the wavelength of the light, and m is the order (1 for the first minimum, 2 for the second
minimum,... counting from the center out). See Figure 4.6.
Figure 4.6: Single Slit Diffraction Pattern
When light passes through two slits, the two light rays emerging from the slits interfere with
each other and produce interference fringes. The angle to the maxima (bright fringes) in the
interference pattern is given by
23
d sin θ = mλ
(m = 0, 1, 2, 3, ...)
where d is the slit separation, θ is the angle from the center of the pattern to the mth
maximum, λ is the wavelength of the light, and m is the order (0 for the central maximum,
1 for the first side maximum, 2 for the second side maximum,... counting from the center
out). See Figure 4.7.
Figure 4.7: Interference Fringes
Setup
1. Set up the laser at one end of the optics bench and place the Multiple Slit Disk in its
holder about 3cm in front of the laser. See Figure 4.8.
Figure 4.8: Optics Bench Setup
2. Cover the screen with a sheet of paper and attach it to the other end of the bench so that
the paper faces the laser.
3. Select the single-double slit comparison by roatting the slit disk until the desired slit set
is centered in the slit holder. Adjust the position of the laser beam from left-to-right and
24
up-and-down until the beam is centered on the slit set so that both the single slit and the
double slit are illuminated simultaneously. The patterns from the single and double slits
should be vertical and side-by-side on the screen.
Procedure
1. Sketch the two side-by-side patterns roughly to scale.
2. Rotate the slit disk to the next comparison set (2 double slits with the same slit width
but different slit separations). Sketch the two side-by-side patterns roughly to scale.
3. Rotate the slit disk to the next comparison set (2 double slits with the same slit separation
but different slit widths). Sketch the two side-by-side patterns roughly to scale.
4. Rotate the slit disk to the next comparison set (double slits/triple slits with the same slit
separation and same slit widths). Sketch the two side-by-side patterns roughly to scale.
5. Replace the Multiple Slit Disk with the Single Slit Disk. Sselect the line/slit comparison.
Sketch the two side-by-side patterns roughly to scale.
6. Select the dot pattern on the Single Slit Disk. Sketch the resulting diffraction pattern
roughly to scale.
7. Select the hole pattern on the Single Slit Disk. Sketch the resulting diffraction pattern
roughly to scale.
Questions
1. What are the similarities and differences between the single slit and the double slit?
2. How does the double slit pattern change when the slit separation is increased?
3. How does the double slit pattern change when the slit width is increased?
4. What differences are there between a double slit pattern and a triple slit pattern?
5. How does the diffraction pattern from a slit differ from the diffraction pattern from a
line?
6. How does the diffraction pattern from the dot pattern differ from the diffraction pattern
from the hole pattern?
25
Chapter 5
MICROWAVE OPTICS
Experiment 1: Refraction Through A Prism
Equipment Needed
Transmitter
Goniometer
Receiver
Rotating Table
Protractor
Ethafoam Prism mold with styrene pellets
Theory
An electromagnetic wave usually travels in a straight line. As it crosses a boundary between
two different media, however, the direction of propagation of the wave changes. This change
in direction is called Refraction, and it is summarized by a mathematical relationship
known as the Law of Refraction (otherwise known as Snell’s Law):
n1 sin θ1 = n2 sin θ2
where θ1 is the angle between the direction of propagation of the incident wave and the normal
to the boundary between the two media, and, θ2 is the corresponding angle for the refracted
wave (see Figure 5.1). Every material can be described by a number n, called its Index of
Refraction. This number indicates the ratio between the speed of electromagnetic waves
in vacuum and the speed of electromagnetic waves in the material, also called the medium.
In general, the media on either side of a boundary will have different indeces of refraction.
Here they are labeled n1 and n2 . It is the difference between indeces of refraction (and the
difference between wave velocities this implies) which causes ”bending”, or refraction of a
wave as it crosses the boundary between two distinct media.
26
Figure 5.1: Angles of Incidence and Refraction
In this experiment, you will use the law of refraction to measure the index of refraction for
styrene pellets.
Procedure
1. Arrange the equipment as shown in Figure 5.2. Rotate the empty prism mold and see
how it effects the incident wave. Does it reflect, refract, or absorb the wave?
Figure 5.2: Equipment Setup
2. Fill the prism mold with the styrene pellets. To simplify the calculations, align the face of
the prism that is nearest to the Transmitter perpendicular to the incident microwave beam.
27
3. Rotate the movable arm of the Goniometer and locate the angle θ at which the refracted
signal is a maximum.
NOTE: θ is just the angle that you read directly from the Degree Scale of the Goniometer.
θ = ........................
Figure 5.3: Geometry of Prism Refraction
4. Using the diagram shown in Figure 5.3, determine θ1 and use your value of θ to determine
θ2 . (You will need to use a protractor to measure the Prism angles.)
θ1 = ........................
θ2 = ........................
5. Plug these values into the Law of Refraction to determine the values of n1 /n2 .
n1 /n2 = ........................
6. The index of refraction for air is equal to 1.00. Use this fact to determine n1 , the index
of refraction for the styrene pellets.
Questions
1. In the diagram of Figure 5.3, the assumption is made that the wave is unrefracted when it
strikes the first side of the prism (at an angle of incidence of 0o ). Is this a valid assumption?
28
2. Using this apparatus, how might you verify that the index of refraction for air is equal to
one.
3. Would you expect the refraction index of the styrene pellets in the prism mold to be the
same as for a solid styrene prism?
29
Experiment 2: Fabry-Perot Interferometer
Equipment Needed
Transmitter
Goniometer
Receiver
Partial Reflectors(2)
Component Holders (2)
Theory
When an electromagnetic wave encounters a partial reflector, part of the wave reflects and
part of the wave transmits through the partial reflector. A Fabry-Perot Interferometer
consists of two parallel partial reflectors positioned between a wave source and a detector
(see Figure 5.4).
Figure 5.4: Fabry-Perot Interferometer
The wave from the source reflects back and forth between the two partial reflectors. However,
with each pass, some of the radiation passes through to the detector. If the distance between
the partial reflectors is equal to nλ/2, where λ is the wavelength of the radiation and n is an
integer, then all the waves passing through to the detector at any instant will be in phase.
In this case, a maximum signal will be detected by the Receiver. If the distance between the
partial reflectors is not a multiple of λ/2, then some degree of destructive interference will
occur, and the signal will not be a maximum.
Procedure
1. Arrange the equipment as shown in Figure. Plug in the Transmitter and adjust the
Receiver controls for an easily readable signal.
30
2. Adjust the distance between the Partial Reflectors and observe the relative minima and
maxima.
3. Adjust the distance between the Partial Reflectors to obtain a maximum meter reading.
Record, d1 , the distance between the reflectors.
d1 = .....................
4. While watching the meter, slowly move one Reflector away from the other. Move the
Reflector until the meter reading has passed through at least 10 minima and returned to
a maximum. Record the number of minima that were traversed. Also record d2 , the new
distance between the Reflectors.
Minima traversed = .....................
d2 = .....................
5. Use your data to calculate λ, the wavelength of the microwave radiation.
λ = .....................
6. Repeat your measurements, beginning with a different distance between the Partial
Reflectors.
d1 = .....................
d2 = .....................
Minima traversed = .....................
λ = .....................
Questions
1. What spacing between the two Partial Reflectors shoul cause a minimum signal to be
delivered to the Receiver?
2. In an optical Fabry-Perot interferometer pattern usually appears as a series of concentric
rings. Do you expect such a pattern to occur here? Why? Check to see if there is one.
31
Experiment 3: Michelson Interferometer
Equipment Needed
Transmitter
Goniometer
Receiver
Partial Reflector(1)
Component Holders (2)
Fixed Arm Assembly
Rotating Table, Reflectors (2)
Theory
Like the Fabry-Perot interferometer, the Michelson interferometer splits a single wave, then
brings the constituent waves back together so that they superpose, forming an interference
pattern. Figure shows the setup for the Michelson interferometer. A and B are Reflectors
and C is a Partial Reflector. Microwaves travel from the Transmitter to the Receiver over
two different paths. In one path, the wave passes directly through C, reflects back to C from
A, and then is reflected from C into the Receiver. In the other path, the wave reflects from
C into B, and then back through C into the Receiver.
If the two waves are in phase when they reach the Rreceiver, a maximum signal is detected.
By moving one of the Reflectors, the path length of one wave changes, thereby changing its
phase at the Receiver so a maximum is no longer detected. Since each wave passes twice
between a Reflector and the Partial Reflector, moving a Reflector a distance λ/2 will cause a
complete 360-degree change in the phase of one wave at the Receiver. This causes the meter
reading to pass through a minimum and return to a maximum.
Procedure
1. Arrange the equipment as shown in Figure 5.5. Plug in the Transmitter and adjust the
Receiver for an easily readable signal.
2. Slide Reflector A along the Goniometer arm and observe the relative maxima and minima
of the meter deflections.
3. Set Reflector A to a position which produces a maximum meter reading. Record, x1 , the
position of the Reflector on the Goniometer arm.
x1 = .....................
4. While watching the meter, slowly move Reflector A away from the Partial Reflector. Move
the Reflector until the meter reading has passed through at least 10 minima and returned
32
Figure 5.5: Michelson Interferometer
to a maximum. Record the number of minima that were traversed. Also record x2 , the new
position of Reflector A on the Goniometer arm.
Minima traversed = ....................
x2 = .....................
5. Use your data to calculate λ, the wavelength of the microwave radiation.
λ = .....................
6. Repeat your measurements, beginning with a different position for Reflector A.
x1 = .....................
Minima traversed = ....................
x2 = .....................
λ = .....................
33
Question
You have used the interferometer to measure the wavelength of the microwave radiation. If
you already knew the wavelength, you could use the interferometer to measure the distance
over which the Reflector moved. Why would an optical interferometer (an interferometer
using visible light rather than microwaves) provide better resolution when measuring distance
than a microwave interferometer?
An Idea for Further Investigation
Place a cardboard box between the Partial Reflector and Reflector A. Move one of the
reflectors until the meter deflection is a maximum. Slowly fill the box with styrene pellets
while observing the meter deflections. On the basis of these observations, adjust the position
of Reflector A to restore the original maximum. Measure the distance over which you
adjusted the reflector. Also measure the distance traversed by the beam through the pellets.
From this data, can you determine the styrene pellets’ index of refraction at microwave
frequencies? (The wavelength of electromagnetic radiation in a material is given by the
relationship λ = λo /n; where λ is the wavelength, λo is the wavelength in a vacuum, and n
is the index of refraction of the material). Try boxes of various widths. you might also try
filling them with a different material.
34
CHAPTER 7
SPECTROPHOTOMETRY
Introduction:
In this experiment, you will learn the basic principals of spectrophotometry. A
spectrophotometer is a very powerful tool used in science yet operates by simply shining
a beam of light, filtered to a specific wavelength (or very narrow range of wavelengths),
through a sample and onto a light meter. Some basic properties of the sample can be
determined by the wavelengths and amount of light absorbed by the sample. The aim of
this
experiment
is
to
measure
the
transmission
of
a
sample
by
using
spectrophotometer.
Theory:
Electromagnetic Spectrum:
The electromagnetic
spectrum is
the range of
all
possible
frequencies
of electromagnetic radiation. The "electromagnetic spectrum" of an object is the
characteristic distribution of electromagnetic radiation emitted or absorbed by that
particular object.
The electromagnetic spectrum extends from low frequencies used for
modern radio communication to gamma radiation at the short-wavelength (highfrequency).
Figure.1 Electromagnetic Spectrum
Basic Principle of Spectrophotometry
A spectrophotometer is an instrument that measures the fraction of the incident light
transmitted through a sample. In other words, it is used to measure the amount of light
that passes through a sample material and, by comparison to the initial intensity of light
reaching the sample, they indirectly measure the amount of light absorbed by that
sample.
Spectrophotometers are designed to transmit light of narrow wavelength ranges (see
Figure 1 the electromagnetic spectrum).
A given compound will not absorb all
wavelengths equally–that’s why things are different colors (some compounds absorb
only wavelengths outside of the visible light spectrum, and that’s why there are colorless
solutions like water).
Because different compounds absorb light at different
wavelengths, a spectrophotometer can be used to distinguish compounds by analyzing
the pattern of wavelengths absorbed by a given sample.
When studying a material by spectrophotometry, you put it in a sample holder called a
cuvette and place it in the spectrophotometer as shown in figure 2. Light of a particular
wavelength passes through the sample inside the cuvette and the amount of light
transmitted (passed through the sample—Transmittance) or absorbed (Absorbance) by
the sample is measured by a light meter.
Figure 2. Components of Spectrophotometry
The light from the spectrophotometer’s light source does not consist of a single
wavelength, but a continuous portion of the electromagnetic spectrum. This light is
separated into specific portions of the spectrum through the use of prisms or a diffraction
grating. A small portion of the separated spectrum then passes through a narrow slit.
When you adjust the wavelength on a spectrophotometer, you are changing the position
of the prism or diffraction grating so that different wavelengths of light are directed at the
slit. The smaller the slit width, the better the ability of the instrument to resolve various
compounds. This small band of light then passes through the cuvette containing the
sample. Light that passes through the sample is detected by a photocell and measured
to yield the transmittance or absorbance value (optical density) for the sample.
TRANSMITTANCE and ABSORBANCE
Transmittance :
The transmittance is defined as the ratio of the light energy transmitted through the
sample (P) to the energy transmitted through the reference blank (P0). Since the
compound being tested is not present in the reference blank, the transmittance of the
reference blank is defined as 100%T. This number is multiplied by 100 to determine the
percent transmittance (%T), the percentage of light transmitted by the substance relative
to the reference blank.
Absorbance:
Absorbance is defined as the negative logarithm of the transmittance, and you will note
that absorbance and transmittance bear an inverse relationship.
Absorbance = - log T = - log P/Po
Questions
1. What is transmission?
2. What is absorption?
3. Explain the physics behind the transmission and absorption of a solid. Why does
the some wavelength interval absorbed whereas others not by a given solid?
4. Explain the relationship between absorbance and transmittance?
5. If some of the light is absorbed by the sample…
is P greater than, less than or equal to P0?
is T greater than or less than 1?
6.
Again for sample A and B, which would have higher transmittance and absorbance?
Explain your reasoning.
7. Explain the terms opaque, translucent and transparent. What is difference
between them? Give an example of each one.
8. A light with wavelength 400 nm is sent to a solid with 1.1 eV bandgap energy.
What do you expect? Does the light absorbed or transmitted?